Polynomial solutions of a nonlinear difference equation

A class of nonlinear difference equations is considered. We show how their polynomial solutions can be computed in a systematic manner.     

Editorial for Focus Issue on Optical3D Display and Imaging

正With the impressive progress of flat panel display technologies,the three-dimensional(3D)display and imaging technologies have attracted much attention in recent years as they can provide ultimate realistic views to us.Hence we designed a focus issue intended to introduce recent optical researches in this field,especially the works by some distinguished research groups.     

光谱法锌离子检测系统的研究

采取标准锌显色剂与锌发生显色反应，生成不溶于水的絮状络合物。用光谱仪测它的吸光度，研究其特征谱与吸光度的特点，建立其浓度与特征波长吸光度间的数学模型。本文所采用的显色剂主要与锌、铜、镉、镍四种离子发生络合反应。因此分别探索了四种离子高浓度以及低浓度时显色反应的吸光度，最终通过得到锌离子浓度与吸光度的关系式以及锌离子浓度与四波长下四种离子混合溶液显色后的吸光度的关系式，给出了锌离子的吸光度与总吸光度的关系式。显色反应能否满足分光光度法的要求，主要与显色剂的性质有关，同时显色反应的条件也至关重要。因为在显色反应过程中，主要是锌离子与锌显色剂发生络合反应形成络离子，进而形成絮状络合物。络离子一般比较稳定，但在水溶液中也存在着电离平衡，也就是说当显色条件发生变化时，既有可能形成络离子，也有可能发生络离子的分解，从而影响络合反应的程度。显色条件包括显色剂用量、pH值、反应温度、显色时间、待测溶液的盐度以及浊度等。重点研究待测溶液的盐度对锌离子浓度测量值的影响，并通过实验给出影响规律以及校正模型。     

Solvent replacement to thermo‐responsive nanoparticles from long‐subchain hyperbranched PSt grafted with PNIPAM for encapsulation

Long‐subchain hyperbranched polystyrene (lsc‐hp PSt) with uniform subchain length was obtained through copper‐catalyzed azide‐alkyne cycloaddition click chemistry from seesaw macromonomer of PSt having one alkynyl group anchored at the chain centre and two azido group attached to both chain ends [alkynyl‐(PSt‐N₃)₂]. After precipitation fraction, different portions of lsc‐hp PSt having narrow overall molecular weight distribution were obtained for further grafting with alkynyl‐capped poly(N‐isopropylacrylamide) (alkynyl‐PNIPAM), which was obtained via single‐electron transfer living radical polymerization of NIPAM with propargyl 2‐bromoisobutyrate as the initiator and grafted onto the peripheral azido groups of lsc‐hp PSt via click chemistry. Thus, amphiphilic lsc‐hp PSt grafted with PNIPAM chains (lsc‐hp PSt‐g‐PNIPAM) was obtained and would have star‐like conformation in tetrahydrofuran (THF). By replacing THF with water, lsc‐hp PSt‐g‐PNIPAM was dissolved at molecular level in aqueous solution due to the hydrophilicity of PNIPAM and exhibited thermal induced shrinkage of PNIPAM arms. The water‐insoluble lsc‐hp PSt would collapse densely and could be served as a reservoir to absorb hydrophobic chemicals in aqueous solution. The influence of overall molecular weight of lsc‐hp PSt on the absorption of pyrene was studied. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Low-Temperature Electrolyte Design for Lithium-Ion Batteries: Prospect and Challenges

Lithium-ion batteries have dominated the energy market from portable electronic devices to electric vehicles. However, the LIBs applications are limited seriously when they were operated in the cold regions and seasons if there is no thermal protection. This is because the Li+ transportation capability within the electrode and particularly in the electrolyte dropped significantly due to the decreased electrolyte liquidity, leading to a sudden decline in performance and short cycle-life. Thus, design a low-temperature electrolyte becomes ever more important to enable the further applications of LIBs. Herein, we summarize the low-temperature electrolyte development from the aspects of solvent, salt, additives, electrolyte analysis, and performance in the different battery systems. Then, we also introduce the recent new insight about the cation solvation structure, which is significant to understand the interfacial behaviors at the low temperature, aiming to guide the design of a low-temperature electrolyte more effectively.     

Study on an optical system with coherent laser array source and phase optimization in turbulent atmosphere

Model of an optical system with coherent laser array source and the piston phase optimized by the stochastic parallel gradient descent algorithm is established. With this model, theory of beam propagation through the optical system in turbulent atmosphere is analyzed, and the analytical formulas of the beam average intensity along the propagation path are derived. Strehl ratio of the received beam induced by intensity disorderly distribution and power efficiency of the received beam are introduced to evaluate performance of the optical system. Under the H-V 5/7 atmospheric turbulent model, performance of an optical system with determinate parameters was calculated, and the influences of the propagation distance and the laser wavelength were numerically analyzed, respectively.